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<a href="stats_8py.html">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a><a class="code" href="namespaceambhas_1_1stats.html">00001</a> <span class="comment"># -*- coding: utf-8 -*-</span>
<a name="l00002"></a>00002 <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00003"></a>00003 <span class="stringliteral">Created on Thu Dec 29 15:24:08 2011</span>
<a name="l00004"></a>00004 <span class="stringliteral"></span>
<a name="l00005"></a>00005 <span class="stringliteral">@author: Sat Kumar Tomer</span>
<a name="l00006"></a>00006 <span class="stringliteral">@website: www.ambhas.com</span>
<a name="l00007"></a>00007 <span class="stringliteral">@email: satkumartomer@gmail.com</span>
<a name="l00008"></a>00008 <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00009"></a>00009 
<a name="l00010"></a>00010 <span class="keyword">from</span> __future__ <span class="keyword">import</span> division
<a name="l00011"></a>00011 <span class="keyword">import</span> numpy <span class="keyword">as</span> np
<a name="l00012"></a>00012 <span class="keyword">import</span> statistics <span class="keyword">as</span> st
<a name="l00013"></a>00013 <span class="keyword">from</span> scipy.interpolate <span class="keyword">import</span> interp1d
<a name="l00014"></a>00014 <span class="keyword">from</span> scipy.stats <span class="keyword">import</span> norm, chi2
<a name="l00015"></a>00015 <span class="keyword">from</span> scipy.stats <span class="keyword">import</span> scoreatpercentile
<a name="l00016"></a>00016 
<a name="l00017"></a><a class="code" href="namespaceambhas_1_1stats.html#a8e91bdaed3f65151e9835222afe07106">00017</a> <span class="keyword">def </span><a class="code" href="namespaceambhas_1_1stats.html#a8e91bdaed3f65151e9835222afe07106">bias_correction</a>(oc, mc, mp):
<a name="l00018"></a>00018     <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00019"></a>00019 <span class="stringliteral">    Input:</span>
<a name="l00020"></a>00020 <span class="stringliteral">        oc: observed current</span>
<a name="l00021"></a>00021 <span class="stringliteral">        mc: modeled current</span>
<a name="l00022"></a>00022 <span class="stringliteral">        mp: modeled prediction     </span>
<a name="l00023"></a>00023 <span class="stringliteral">    </span>
<a name="l00024"></a>00024 <span class="stringliteral">    Output:</span>
<a name="l00025"></a>00025 <span class="stringliteral">        mp_adjusted: adjusted modeled prediction</span>
<a name="l00026"></a>00026 <span class="stringliteral">        </span>
<a name="l00027"></a>00027 <span class="stringliteral">        </span>
<a name="l00028"></a>00028 <span class="stringliteral">    &quot;&quot;&quot;</span>
<a name="l00029"></a>00029     
<a name="l00030"></a>00030     <span class="comment"># convert the input arrays into one dimension</span>
<a name="l00031"></a>00031     oc = oc.flatten()
<a name="l00032"></a>00032     mc = mc.flatten()
<a name="l00033"></a>00033     mp = mp.flatten()    
<a name="l00034"></a>00034     
<a name="l00035"></a>00035     <span class="comment"># Instead of directly inverting the CDF, linear interpolation using </span>
<a name="l00036"></a>00036     <span class="comment"># interp1d is used to invert the CDF.</span>
<a name="l00037"></a>00037     
<a name="l00038"></a>00038     F_oc, OC = st.cpdf(oc, n=1000)
<a name="l00039"></a>00039     f = interp1d(F_oc, OC)
<a name="l00040"></a>00040     
<a name="l00041"></a>00041     F1 = st.cpdf(mc, mp)
<a name="l00042"></a>00042     mp_adjusted = f(F1)
<a name="l00043"></a>00043     
<a name="l00044"></a>00044     <span class="keywordflow">return</span> mp_adjusted
<a name="l00045"></a>00045 
<a name="l00046"></a>00046 
<a name="l00047"></a><a class="code" href="namespaceambhas_1_1stats.html#afbdebc3c7affb6d8a317dc396294d21c">00047</a> <span class="keyword">def </span><a class="code" href="namespaceambhas_1_1stats.html#afbdebc3c7affb6d8a317dc396294d21c">mk_test</a>(x, alpha = 0.05):
<a name="l00048"></a>00048     <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00049"></a>00049 <span class="stringliteral">    this perform the MK (Mann-Kendall) test to check if there is any trend present in </span>
<a name="l00050"></a>00050 <span class="stringliteral">    data or not</span>
<a name="l00051"></a>00051 <span class="stringliteral">    </span>
<a name="l00052"></a>00052 <span class="stringliteral">    Input:</span>
<a name="l00053"></a>00053 <span class="stringliteral">        x:   a vector of data</span>
<a name="l00054"></a>00054 <span class="stringliteral">        alpha: significance level</span>
<a name="l00055"></a>00055 <span class="stringliteral">    </span>
<a name="l00056"></a>00056 <span class="stringliteral">    Output:</span>
<a name="l00057"></a>00057 <span class="stringliteral">        trend: tells the trend (increasing, decreasing or no trend)</span>
<a name="l00058"></a>00058 <span class="stringliteral">        h: True (if trend is present) or False (if trend is absence)</span>
<a name="l00059"></a>00059 <span class="stringliteral">        p: p value of the sifnificance test</span>
<a name="l00060"></a>00060 <span class="stringliteral">        z: normalized test statistics </span>
<a name="l00061"></a>00061 <span class="stringliteral">        </span>
<a name="l00062"></a>00062 <span class="stringliteral">    Examples</span>
<a name="l00063"></a>00063 <span class="stringliteral">    --------</span>
<a name="l00064"></a>00064 <span class="stringliteral">      &gt;&gt;&gt; x = np.random.rand(100)</span>
<a name="l00065"></a>00065 <span class="stringliteral">      &gt;&gt;&gt; trend,h,p,z = mk_test(x,0.05) </span>
<a name="l00066"></a>00066 <span class="stringliteral">    &quot;&quot;&quot;</span>
<a name="l00067"></a>00067     n = len(x)
<a name="l00068"></a>00068     
<a name="l00069"></a>00069     <span class="comment"># calculate S </span>
<a name="l00070"></a>00070     s = 0
<a name="l00071"></a>00071     <span class="keywordflow">for</span> k <span class="keywordflow">in</span> xrange(n-1):
<a name="l00072"></a>00072         <span class="keywordflow">for</span> j <span class="keywordflow">in</span> xrange(k+1,n):
<a name="l00073"></a>00073             s += np.sign(x[j] - x[k])
<a name="l00074"></a>00074     
<a name="l00075"></a>00075     <span class="comment"># calculate the unique data</span>
<a name="l00076"></a>00076     unique_x = np.unique(x)
<a name="l00077"></a>00077     g = len(unique_x)
<a name="l00078"></a>00078     
<a name="l00079"></a>00079     <span class="comment"># calculate the var(s)</span>
<a name="l00080"></a>00080     <span class="keywordflow">if</span> n == g: <span class="comment"># there is no tie</span>
<a name="l00081"></a>00081         var_s = (n*(n-1)*(2*n+5))/18
<a name="l00082"></a>00082     <span class="keywordflow">else</span>: <span class="comment"># there are some ties in data</span>
<a name="l00083"></a>00083         tp = np.zeros(unique_x.shape)
<a name="l00084"></a>00084         <span class="keywordflow">for</span> i <span class="keywordflow">in</span> xrange(len(unique_x)):
<a name="l00085"></a>00085             tp[i] = sum(unique_x[i] == x)
<a name="l00086"></a>00086         var_s = (n*(n-1)*(2*n+5) + np.sum(tp*(tp-1)*(2*tp+5)))/18
<a name="l00087"></a>00087     
<a name="l00088"></a>00088     <span class="keywordflow">if</span> s&gt;0:
<a name="l00089"></a>00089         z = (s - 1)/np.sqrt(var_s)
<a name="l00090"></a>00090     <span class="keywordflow">elif</span> s == 0:
<a name="l00091"></a>00091             z = 0
<a name="l00092"></a>00092     <span class="keywordflow">elif</span> s&lt;0:
<a name="l00093"></a>00093         z = (s + 1)/np.sqrt(var_s)
<a name="l00094"></a>00094     
<a name="l00095"></a>00095     <span class="comment"># calculate the p_value</span>
<a name="l00096"></a>00096     p = 2*(1-norm.cdf(abs(z))) <span class="comment"># two tail test</span>
<a name="l00097"></a>00097     h = abs(z) &gt; norm.ppf(1-alpha/2) 
<a name="l00098"></a>00098     
<a name="l00099"></a>00099     <span class="keywordflow">if</span> (z&lt;0) <span class="keywordflow">and</span> h:
<a name="l00100"></a>00100         trend = <span class="stringliteral">&#39;decreasing&#39;</span>
<a name="l00101"></a>00101     <span class="keywordflow">elif</span> (z&gt;0) <span class="keywordflow">and</span> h:
<a name="l00102"></a>00102         trend = <span class="stringliteral">&#39;increasing&#39;</span>
<a name="l00103"></a>00103     <span class="keywordflow">else</span>:
<a name="l00104"></a>00104         trend = <span class="stringliteral">&#39;no trend&#39;</span>
<a name="l00105"></a>00105         
<a name="l00106"></a>00106     <span class="keywordflow">return</span> trend, h, p, z
<a name="l00107"></a>00107 
<a name="l00108"></a><a class="code" href="namespaceambhas_1_1stats.html#acf680ac025b1a963c8b6fcefbc7b7527">00108</a> <span class="keyword">def </span><a class="code" href="namespaceambhas_1_1stats.html#acf680ac025b1a963c8b6fcefbc7b7527">independant</a>(x,y, alpha = 0.05):
<a name="l00109"></a>00109     <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00110"></a>00110 <span class="stringliteral">    this program calculates check if the joint cdf == multiplication of marginal</span>
<a name="l00111"></a>00111 <span class="stringliteral">    distribution or not </span>
<a name="l00112"></a>00112 <span class="stringliteral">    using the chi-squared test </span>
<a name="l00113"></a>00113 <span class="stringliteral">        </span>
<a name="l00114"></a>00114 <span class="stringliteral">    Input:</span>
<a name="l00115"></a>00115 <span class="stringliteral">        x:   a vector of data</span>
<a name="l00116"></a>00116 <span class="stringliteral">        y:   a vector of data</span>
<a name="l00117"></a>00117 <span class="stringliteral">        alpha: significance level</span>
<a name="l00118"></a>00118 <span class="stringliteral">    </span>
<a name="l00119"></a>00119 <span class="stringliteral">    Output:</span>
<a name="l00120"></a>00120 <span class="stringliteral">        ind: True (if independant) False (if dependant)</span>
<a name="l00121"></a>00121 <span class="stringliteral">        p: p value of the significance test</span>
<a name="l00122"></a>00122 <span class="stringliteral">        </span>
<a name="l00123"></a>00123 <span class="stringliteral">    Examples</span>
<a name="l00124"></a>00124 <span class="stringliteral">    --------</span>
<a name="l00125"></a>00125 <span class="stringliteral">      &gt;&gt;&gt; x = np.random.rand(100)</span>
<a name="l00126"></a>00126 <span class="stringliteral">      &gt;&gt;&gt; y = np.random.rand(100)</span>
<a name="l00127"></a>00127 <span class="stringliteral">      &gt;&gt;&gt; ind,p = independant(x,y,0.05)  </span>
<a name="l00128"></a>00128 <span class="stringliteral">    &quot;&quot;&quot;</span>
<a name="l00129"></a>00129     
<a name="l00130"></a>00130     <span class="comment"># calculate the 2D histogram </span>
<a name="l00131"></a>00131     H, xedges, yedges = np.histogram2d(x, y, bins=5)
<a name="l00132"></a>00132     
<a name="l00133"></a>00133     <span class="comment"># calculate the expected values</span>
<a name="l00134"></a>00134     expected_values = np.zeros(H.shape)
<a name="l00135"></a>00135     <span class="keywordflow">for</span> i <span class="keywordflow">in</span> range(H.shape[0]):
<a name="l00136"></a>00136         <span class="keywordflow">for</span> j <span class="keywordflow">in</span> range(H.shape[1]):
<a name="l00137"></a>00137             expected_values[i,j] = H.sum(axis=1)[i]*H.sum(axis=0)[j]/H.sum()
<a name="l00138"></a>00138     
<a name="l00139"></a>00139     <span class="comment"># calculate the chi-squared statistics</span>
<a name="l00140"></a>00140     err_chi2 = ((H-expected_values)**2/expected_values).sum()
<a name="l00141"></a>00141     
<a name="l00142"></a>00142     <span class="comment"># degree of freedom</span>
<a name="l00143"></a>00143     dof = (H.shape[0]-1)*(H.shape[1]-1)
<a name="l00144"></a>00144     
<a name="l00145"></a>00145     <span class="comment"># calculate the p_value</span>
<a name="l00146"></a>00146     rv = chi2(dof)
<a name="l00147"></a>00147     p = 2*(1-rv.sf(err_chi2)) <span class="comment"># two tail test</span>
<a name="l00148"></a>00148     
<a name="l00149"></a>00149     <span class="comment"># test </span>
<a name="l00150"></a>00150     ind = p &gt;= alpha        
<a name="l00151"></a>00151         
<a name="l00152"></a>00152     <span class="keywordflow">return</span> ind, p
<a name="l00153"></a>00153 
<a name="l00154"></a>00154 
<a name="l00155"></a><a class="code" href="classambhas_1_1stats_1_1SpatOutlier.html">00155</a> <span class="keyword">class </span><a class="code" href="classambhas_1_1stats_1_1SpatOutlier.html">SpatOutlier</a>():
<a name="l00156"></a>00156     <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00157"></a>00157 <span class="stringliteral">    this class identify the outliers from the given spatial data of point values</span>
<a name="l00158"></a>00158 <span class="stringliteral">    &quot;&quot;&quot;</span>
<a name="l00159"></a>00159     
<a name="l00160"></a><a class="code" href="classambhas_1_1stats_1_1SpatOutlier.html#ae600249e9fcbda069e9fbad0ba6983ef">00160</a>     <span class="keyword">def </span><a class="code" href="classambhas_1_1stats_1_1SpatOutlier.html#ae600249e9fcbda069e9fbad0ba6983ef">__init__</a>(self,rain):
<a name="l00161"></a>00161         <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00162"></a>00162 <span class="stringliteral">        Input:</span>
<a name="l00163"></a>00163 <span class="stringliteral">            rain:   rain at different spatial locations and time</span>
<a name="l00164"></a>00164 <span class="stringliteral">            time ==&gt; is defined in the first dimension</span>
<a name="l00165"></a><a class="code" href="classambhas_1_1stats_1_1SpatOutlier.html#aec2b15b0062794eee851810e08fdd99a">00165</a> <span class="stringliteral">            space ==&gt; is defined in the second dimension</span>
<a name="l00166"></a>00166 <span class="stringliteral">        &quot;&quot;&quot;</span>
<a name="l00167"></a>00167         <span class="comment"># check for the number of dimension</span>
<a name="l00168"></a>00168         <span class="keywordflow">if</span> rain.ndim &gt; 2:
<a name="l00169"></a>00169             <span class="keywordflow">raise</span> ValueError(<span class="stringliteral">&#39;The dimension of the input should be less than or equal to 2 (two)&#39;</span>)
<a name="l00170"></a>00170         <span class="keywordflow">elif</span> rain.ndim == 1:
<a name="l00171"></a>00171             rain.shape = (1,-1)
<a name="l00172"></a>00172         self.<a class="code" href="classambhas_1_1stats_1_1SpatOutlier.html#aec2b15b0062794eee851810e08fdd99a">rain</a> = rain
<a name="l00173"></a>00173             
<a name="l00174"></a>00174     <span class="keyword">def </span>_identify_outlier(self,threshold=2.0):
<a name="l00175"></a>00175         <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00176"></a>00176 <span class="stringliteral">        Input:</span>
<a name="l00177"></a><a class="code" href="classambhas_1_1stats_1_1SpatOutlier.html#a212e9d519dd3efa62ed8467d0f77c8cf">00177</a> <span class="stringliteral">            threshold: threshold above which the data will be termed as outlier</span>
<a name="l00178"></a>00178 <span class="stringliteral">        &quot;&quot;&quot;</span>
<a name="l00179"></a>00179         rain = self.<a class="code" href="classambhas_1_1stats_1_1SpatOutlier.html#aec2b15b0062794eee851810e08fdd99a">rain</a>
<a name="l00180"></a>00180         q_25 = scoreatpercentile(rain.T,25)
<a name="l00181"></a>00181         q_75 = scoreatpercentile(rain.T,75)
<a name="l00182"></a>00182         q_50 = scoreatpercentile(rain.T,50)
<a name="l00183"></a>00183         
<a name="l00184"></a>00184         q_25_m = np.tile(q_25,(rain.shape[1],1)).T
<a name="l00185"></a>00185         q_50_m = np.tile(q_50,(rain.shape[1],1)).T
<a name="l00186"></a>00186         q_75_m = np.tile(q_75,(rain.shape[1],1)).T
<a name="l00187"></a>00187         
<a name="l00188"></a>00188         index = np.abs(rain-q_50_m)/(q_75_m-q_25_m)
<a name="l00189"></a>00189         self.<a class="code" href="classambhas_1_1stats_1_1SpatOutlier.html#a4b5bb747042f8c4e0228afa60c358bbb">index</a> = index
<a name="l00190"></a>00190         
<a name="l00191"></a>00191         self.<a class="code" href="classambhas_1_1stats_1_1SpatOutlier.html#a212e9d519dd3efa62ed8467d0f77c8cf">outliers</a> = index&gt;=threshold
<a name="l00192"></a>00192     
<a name="l00193"></a><a class="code" href="classambhas_1_1stats_1_1SpatOutlier.html#a826d8579b25e76a53c18617ff226f575">00193</a>     <span class="keyword">def </span><a class="code" href="classambhas_1_1stats_1_1SpatOutlier.html#a826d8579b25e76a53c18617ff226f575">fill_with_nan</a>(self):
<a name="l00194"></a>00194         <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00195"></a>00195 <span class="stringliteral">        this method fills the outliers with the nan</span>
<a name="l00196"></a>00196 <span class="stringliteral">        </span>
<a name="l00197"></a>00197 <span class="stringliteral">        Output:</span>
<a name="l00198"></a>00198 <span class="stringliteral">            rain_filled:    rain filled with nan where outliers were present</span>
<a name="l00199"></a>00199 <span class="stringliteral">        &quot;&quot;&quot;</span>
<a name="l00200"></a>00200         self.<a class="code" href="classambhas_1_1stats_1_1SpatOutlier.html#a5264bcfcf8516cb0a8f7688d32871caf">_identify_outlier</a>()
<a name="l00201"></a>00201         
<a name="l00202"></a>00202         rain_filled = self.<a class="code" href="classambhas_1_1stats_1_1SpatOutlier.html#aec2b15b0062794eee851810e08fdd99a">rain</a>
<a name="l00203"></a>00203         rain_filled[self.<a class="code" href="classambhas_1_1stats_1_1SpatOutlier.html#a212e9d519dd3efa62ed8467d0f77c8cf">outliers</a>] = np.nan
<a name="l00204"></a>00204         <span class="keywordflow">return</span> rain_filled
<a name="l00205"></a>00205 
<a name="l00206"></a>00206 <span class="keywordflow">if</span> __name__ == <span class="stringliteral">&quot;__main__&quot;</span>:
<a name="l00207"></a><a class="code" href="namespaceambhas_1_1stats.html#a622bc6280469add9586c78965d6e1325">00207</a>     oc = np.random.randn(100)
<a name="l00208"></a><a class="code" href="namespaceambhas_1_1stats.html#ab4e58965cf370e19e8ad36308377e7ea">00208</a>     mc = 2+np.random.randn(100)
<a name="l00209"></a><a class="code" href="namespaceambhas_1_1stats.html#a9db52336d307e0fe4a03458cc51918da">00209</a>     mp = 2+np.random.randn(1000)
<a name="l00210"></a>00210     
<a name="l00211"></a>00211     print(<span class="stringliteral">&quot;mean of observed current is %f&quot;</span>%oc.mean())
<a name="l00212"></a>00212     print(<span class="stringliteral">&quot;mean of modeled current is %f&quot;</span>%mc.mean())
<a name="l00213"></a>00213     print(<span class="stringliteral">&quot;mean of modeled prediction is %f&quot;</span>%mp.mean())
<a name="l00214"></a>00214      
<a name="l00215"></a><a class="code" href="namespaceambhas_1_1stats.html#a1a73f1989c31d0307d1bc820f4d8f419">00215</a>     mp_adjusted = <a class="code" href="namespaceambhas_1_1stats.html#a8e91bdaed3f65151e9835222afe07106">bias_correction</a>(oc, mc, mp)
<a name="l00216"></a>00216     print(<span class="stringliteral">&quot;mean of adjusted modeled prediction is %f&quot;</span>%mp_adjusted.mean())
<a name="l00217"></a>00217     
<a name="l00218"></a>00218     <span class="comment"># check the SpatOutlier class</span>
<a name="l00219"></a><a class="code" href="namespaceambhas_1_1stats.html#a5d1c5af321d9d15e222de6b56494a60e">00219</a>     x = np.random.randn(5,20)
<a name="l00220"></a>00220     x[4,4] = 2.9
<a name="l00221"></a><a class="code" href="namespaceambhas_1_1stats.html#ad182b5e8936e83d57cdad9e08a8ad45a">00221</a>     foo = <a class="code" href="classambhas_1_1stats_1_1SpatOutlier.html">SpatOutlier</a>(x)
<a name="l00222"></a><a class="code" href="namespaceambhas_1_1stats.html#a7ca3022b35ac9d8986d901f35b84b987">00222</a>     x1 = foo.fill_with_nan()
<a name="l00223"></a>00223     <span class="keywordflow">print</span> x1[4,4]
<a name="l00224"></a>00224 
<a name="l00225"></a>00225     
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